Transmission electron microtomography without the “missing wedge” for quantitative structural analysis
Introduction
With rapid advances in transmission electron microtomography (TEMT) in materials science [1], [2], there is a growing need for quantitative structural analyses using novel tools. In order to derive important parameters for material developments, such as the volume fraction or interface area, high-quality three-dimensional (3D) reconstructed images without any artifacts are required.
One of the serious factors that limit the TEMT resolution is the “missing wedge” in Fourier space caused by the limitation of the angular range available in a transmission electron microscope (TEM) [3]. Note that computerized tomography (CT), on which TEMT is based, requires projections from entire tilt angles, i.e., ±90°. One way to overcome this problem is to restore data by computing projections inside the missing wedge [4], [5], [6]. An alternative way is to employ “dual-axis TEMT”, in which an additional tilt axis perpendicular to the original axis is used [7], [8], [9]. By this method, the missing volume in the Fourier space becomes a pyramid, which is significantly smaller than the wedge found in the single-axis method, and hence the quality of the reconstructed image is significantly improved.
Although the most faithful tactics for the CT is to tilt the specimen over ±90°, a special specimen holder (e.g., see Ref. [10]) may be required to achieve such a wide angular range for the specimen tilting. Furthermore, as discussed elsewhere [11], the electron path length of a conventional flat thin section geometrically increases and thus the transmission of electrons decreases with the increasing tilt angle. Obviously, the decrease in the transmission causes deterioration of the projections, which negatively affects the 3D reconstruction. It was shown that one could prevent the increase in the electron path length by using a square-prism-shaped section [11]. However, even in the case of the square-prism-shaped section, image recording at a very high tilt angle, e.g., 80° or more, becomes quite difficult since the sections are normally placed on copper grids that hinder the section at such high tilt angles. Thus, ideally, a cylindrical or spherical specimen without any supporting grid (or film) is best suited for the complete (±90°) tilting.
In the present study, a rod-shaped specimen, whose diameter is ca. 150 nm, was attached at the tip of a specially modified specimen holder without any supporting film. As will be shown later, this arrangement enabled us to freely rotate the rod-shaped specimen with a high precision. The rod-shaped specimen was fabricated by a focused ion beam (FIB) method, applicability of which to polymer materials have recently been confirmed [12]. A complete set of tomograms has been generated from 181 projections that were taken over the angular range of ±90° on a nanometer scale. The volume fraction and the surface area of the fillers in the nanocomposite were evaluated as a function of the maximum tilt angles, and the error associated with the insufficient sampling was quantitatively characterized and discussed.
Section snippets
Experimental details
The polymer nanocomposite was prepared by a conventional direct dispersion method with ultrafine zirconium dioxide (zirconia) particles and a thermally stable polymer [13]. The size of the zirconia was 5–20 nm, and the volume concentration was ca. 5% in raw materials.
An FIB system (FB2100, Hitachi, Ltd., Japan) at an acceleration voltage of 40 kV was used to make a rod-shaped specimen from the nanocomposite. At first, tungsten (W) was deposited on the nanocomposite surface of the bulk material in
Results and discussion
Fig. 3(a) shows an electron micrograph of the rod-shaped specimen. A black region at the tip of the specimen was the tungsten deposited before the fabrication by FIB. The 5–20 nm zirconia grains were observed as black domains in the polymer matrix in the enlarged electron micrograph (Fig. 3(b)). No sign of damage caused in the FIB fabrication process, such as melting by the gallium ion beam or the re-deposition of contaminations, was observed on the surface of the rod-shaped specimen, indicating
Conclusion
A 3D visualization and structural analysis of a zirconia/polymer nanocomposite material were carried out by TEMT with particular emphasis on complete rotation of the specimen, i.e., ±90°. As a result of two improvements in the specimen for the ±90° rotation, i.e., the fabrication of a rod-formed specimen and the modification of the specimen holder, a 3D image with an entirely isotropic resolution was achieved.
A series of 3D reconstructions was made from the same tilt series by limiting the
Acknowledgements
The authors would like to thank Dr. Y. Nishikawa for useful discussions, Mrs. T. Kaneko and K. Sawa for invaluable technical assistance. We also thank Mr. Y. Yamamura, Dr. N. Sadayori, Mr. T. Kondou, and Dr. S. Katayama in NITTO DENKO Corp. for their gift of the polymer nanocomposite sample. And this work was partially supported by New Energy and Industrial Technology Development Organization (NEDO) through Japanese National Project “Nano Structures Polymer Project” and “Development of
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